My son is towards the end of his first year at Montessori. He started at about 21 months, IIRC.
I am not sure that I can give you a very technical answer as to why it is "better," but I can share my experience. I went to Montessori in the early 80s (as did my two siblings). We L O V E D it. Unfortunately, the program went only through Kindergarten age. All three of us have very fond memories of this time and loved the experience. Of course, first grade was a major let down after that! :LOL
Naturally, I wanted the same experience for my kids as well, so I began researching before we made a big move (from MA to FL). It was then I realized that we were moving to where the Montessori Foundation was headquarted! So there is a GREAT school just 10 minutes away from us. There is also a charter school (ie. FREE!) farther away (30 mins) that takes 3 year olds that don't wear diapers.
The cost is a bit hard to swallow at times - $8,500 for full day toddlers thru primary (this school goes through HS). My daughter is starting there in the fall too (about 22 months then), so that will be a big pill. But honestly, I cannot imagine them anywhere else. We actually toured a couple of schools that start at 2 years old and OMG, what a train wreck! Bratty toddlers fighting over playdough, whining, ugh. It was so bad - and these were schools winning "top honors" and charging a pretty penny as well (just not as much as our current school). We needed no convincing that we had to stick where we were.
One of the BIGGEST things that Montessori has taught our son s respect. Respect for everything and everyone. He was (is?) a VERY spiritied child. Walking at 8 months old and never stopping after that. Very strong willed and a bit wild. We believe VERY much in gentle discipline and treating our children with the same respoect that we treat each other (ie. we don't yell at each other, so we don't yell at our kids either). Montessori reinforces these same ideas. I love that he is with 18 month olds to 3+ year olds because they all learn from each other and teach each other things. AJ has thrived there. They teach them life things - like how to set the table (each child must bring a placemat, napkin and silverware for lunch so they can set the table beforehand), sweeping, planting and growing, folding of lanudry, etc. AJ always requests his placemet and napkin for his lap at dinner - he loves the structure of it. He is always thinking of others before himself (at 2.5 years old!). He has a sister 11 months his junior, and if he gets a snack, he ALWAYS makes sure Gracie has one first. He initiates taking turns (makes sure to tell everyone when it is AJ's turn and then tells everyone it is Gracie's turn, etc.). He listens VERY carefully to requests from us and instruction on how to do things. He is incredibly focused and has intense concentration when working on things. Just the other day, his teacher mentioned that AJ took HER trash from lunch and threw it away when she was done - even when he didn't have any of his own. She was floored! They model such compassion and the kids pick that up so well. I love that he has other adult figures in his life that model and reinforce the behavior that we do. It makes our parenting enjoyable since we are not at war with him! I can't wait for our little girl to start too - although I can already see him rubbing off on her.
As far as why it is so expensive...we wondered that too. AJ's class has 9 toddlers and 2 teachers. If they all pay $8,500, that is $76,500 in a year. Let's assume that 1 child pays half tuition because of financial aide - so that is $72,275. I have no clue what the teachers make, but one is a ten year verteran there (been teaching Montessori even longer). Let's say they make 55,000 and 35,000 a piece (and I would like to think that is a LOW estimate). That right there is more that our classroom pays in. Even if you don't assume one child gets assistance. So really, I am paying for a small class size and therefore a higher level of devotion from the teacher (among many other things). I cannot even compare the choas that we saw at the other schools we looked at to his classroom. The Montessori classroom is tranquil and organized. Everything is in its place. All lessons are laid out on shelves and replaced properly by the students. Of course, they are kids and act as such, but there is just something amazing about the sense of calm around them.
For AJ's second birthday, we had his entire class to Gymboree Play and Music. All three teachers separately stopped me at the end to ask where these kids went to school. They said they were the best behaved, best listening group of kids they had ever led there. They attributed this all to their school. I have to agree - there is just something about Montessori kids.

Sorry for the novel...I could go on and on too! If you have any other questions, please let me know!
Laura